I'm wanting to clarify a few points here.

Plumber's putty is NORMALLY used to seal between the sink lip and top of the counter top on a drop-in sink. A gazillion kitchen sinks are installed with plumber's putty under their lips. I really don't know if the same is true for undermount kitchen sinks, or not. My understanding is that undermount kitchen sinks are stuck to the bottom of the counter top with an epoxy adhesive.

Yes, most plumbers probably would use silicone caulk as the sealant under a drop-in kitchen sink, but I won't do that, and haven't done that in any of the 21 kitchen sinks in my building. The reason why is that silicone also works as a good adhesive, and should you ever want to remove that sink in future, to have better access to the plumbing under that sink, having silicone holding it in place is just gonna make it more of a fight to remove. And, besides removing the sink, removing the silicone stuck to the counter top and sink lip is very much more difficult than removing plumber's putty. So, in my building, I use plumber's putty under the lip of ALL of my drop-in kitchen sinks. And, I haven't had a problem with any of them allowing water to leak past the plumber's putty seal between the sink lip and the counter top.

So, if it were me, if this is a drop-in sink, I'd definitely use plumber's putty under the sink's lip.

Someone said that "putty" is simply clay mixed with linseed oil. That is correct. GLAZING putty, which is used on the windows in older homes, is nothing more than linseed oil mixed with clay. Plumber's putty is a different kettle of fish because it doesn't harden the way glazing putty does. If you buy a tub of plumber's putty, the surface of it won't get hard when exposed to air the way glazing putty will. I really don't know the difference between glazing putty and plumber's putty is, but if I had to guess, my guess would be that unlike the linseed oil used in glazing putty, plumber's putty uses a semi-drying oil.

Drying oils are those which dry to a solid when exposed to the oxygen in the air. Such oils include linseed oil, Tung oil, walnut oil, poppyseed oil, oiticia oil, safflower oil, Tall oil (which is a by-product of the pulp and paper industry) and some oils derived from fish.

Non-drying oils are those which don't react with oxygen to transform into a solid at all, and such oils would include crude oil, olive oil, coconut oil, grape seed oil and palm tree oil.

However, there are also "semi-drying" oils with transform from a liquid to a stiff liquid when exposed to the oxygen in the air, and such oils would include soy bean oil.

My guess, and it's only a guess, is that plumber's putty is clay mixed with a semi-drying oil, like soy bean oil. Old plumber's putty is stiff and breaks easily. But, it's not nearly as rigid and brittle as old glazing putty.

So, if this is a drop-in sink, I'd go ahead and use plumber's putty.